Multi-Stage Pricing for Coordination of Thermostatically Controlled Loads: A Dynamic Stackelberg Game Approach

TL;DR

This paper develops a dynamic Stackelberg game model for multi-stage pricing to coordinate thermostatically controlled loads, optimizing social welfare while respecting peak energy constraints, validated with real market data and simulations.

Contribution

It introduces a novel multi-stage pricing framework using a dynamic Stackelberg game approach with a guaranteed convergence algorithm for TCL coordination.

Findings

Effective control strategy validated with real market data

Guaranteed convergence of the pricing algorithm

Demonstrated improvement in social welfare and peak management

Abstract

This paper focuses on multi-stage coordination for a population of thermostatically controlled loads (TCL). Each load maximizes the individual utility in response to an energy price, while the coordinator determines the price to maximize the social welfare subject to a peak energy constraint. The coordination problem is formulated as a dynamic Stackelberg game. The Stackelberg solution is derived using an indirect approach: we first obtain an upper bound of the Stackelberg game, then we prove that this upper bound is attainable. Sufficient conditions for the optimal solution are characterized. Based on these conditions, a pricing algorithm with guaranteed convergence is developed to compute the Stackelberg solution employing the monotonicity of the user responses. Our control strategy is validated using real market data and weather information, and realistic simulation results are presented to demonstrate the effectiveness of the proposed control framework.